Copernican heliocentrism is the astronomical model developed by Nicolaus Copernicus and published in 1543. This model positioned the Sun at the center of the Universe, motionless, with Earth and the other planets orbiting around it in circular paths, modified by epicycles, and at uniform speeds. The Copernican model displaced the geocentric model of Ptolemy that had prevailed for centuries, which had placed Earth at the center of the Universe.
Heliocentric model from Nicolaus Copernicus' De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres)
Nicolai Copernicito Torinensis De Revolutionibus Orbium Coelestium, Libri VI (On the Revolutions of the Heavenly Spheres, in six books) (title page of 2nd edition, Basel, 1566)
Statue of Copernicus next to Cracow University's Collegium Novum
Andreas Cellarius's illustration of the Copernican system, from the Harmonia Macrocosmica (1660)
In the Hipparchian, Ptolemaic, and Copernican systems of astronomy, the epicycle was a geometric model used to explain the variations in speed and direction of the apparent motion of the Moon, Sun, and planets. In particular it explained the apparent retrograde motion of the five planets known at the time. Secondarily, it also explained changes in the apparent distances of the planets from the Earth.
The complexity to be described by the geocentric model
The deferent (O) is offset from the Earth (T). P is the center of the epicycle of the Sun S.